statistics

Find the number of words formed by permuting all the letters
of the word INDEPENDENCE such that the E's do not come together.

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  1. Use the "backdoor" approach,
    that is
    find the number of ways when they are together.

    then we have EEEE, I, N,N,N,D,D,P,C
    arrange 9 things, with 3N's and 2 D's
    = 9!/(3!2!)
    = 30240

    number of arrangements without restriction
    = 12!/(4!3!2!) = 1663200

    so number of ways when they are not together
    = 1663200 - 30240 = 1632960

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